If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:

**A. ** 0

**B. ** 1

**C. ** 2

**D. ** None of these

**Answer : ****Option C**

**Explaination / Solution: **

Sum of digits = (5 + 1 + 7 + *x* + 3 + 2 + 4) = (22 + *x*), which must be divisible by 3.

*x* = 2.

Workspace

Report

The smallest 3 digit prime number is:

**A. ** 101

**B. ** 103

**C. ** 109

**D. ** 113

**Answer : ****Option A**

**Explaination / Solution: **

The smallest 3-digit number is 100, which is divisible by 2.

100 is not a prime number.

√101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

101 is a prime number.

Hence 101 is the smallest 3-digit prime number.

Workspace

Report

Which one of the following numbers is exactly divisible by 11?

**A. ** 235641

**B. ** 245642

**C. ** 315624

**D. ** 415624

**Answer : ****Option D**

**Explaination / Solution: **

(4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.

Workspace

Report

(?) - 19657 - 33994 = 9999

**A. ** 63650

**B. ** 53760

**C. ** 59640

**D. ** 61560

**E. ** None of these

**Answer : ****Option A**

**Explaination / Solution: **

Workspace

Report

The sum of first 45 natural numbers is:

**A. ** 1035

**B. ** 1280

**C. ** 2070

**D. ** 2140

**Answer : ****Option A**

**Explaination / Solution: **

Let S_{n} =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.

S_{n} = | n | [2a + (n - 1)d] | = | 45 | x [2 x 1 + (45 - 1) x 1] | = | 45 | x 46 | = (45 x 23) | ||

2 | 2 | 2 |

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

**Shorcut Method:**

S_{n} = | n(n + 1) | = | 45(45 + 1) | = 1035. |

2 | 2 |

Workspace

Report

Which of the following number is divisible by 24 ?

**A. ** 35718

**B. ** 63810

**C. ** 537804

**D. ** 3125736

**Answer : ****Option D**

**Explaination / Solution: **

24 = 3 x8, where 3 and 8 co-prime.

Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.

Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.

Consider option (D),

Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.

Also, 736 is divisible by 8.

3125736 is divisible by (3 x 8), *i.e.,* 24.

Workspace

Report

753 x 753 + 247 x 247 - 753 x 247 | = ? |

753 x 753 x 753 + 247 x 247 x 247 |

Workspace

Report

(?) + 3699 + 1985 - 2047 = 31111

**A. ** 34748

**B. ** 27474

**C. ** 30154

**D. ** 27574

**E. ** None of these

**Answer : ****Option B**

**Explaination / Solution: **

*x* + 3699 + 1985 - 2047 = 31111

*x* + 3699 + 1985 = 31111 + 2047

*x* + 5684 = 33158

*x* = 33158 - 5684 = 27474.

Workspace

Report

If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:

**A. ** 2

**B. ** 5

**C. ** 6

**D. ** 7

**Answer : ****Option D**

**Explaination / Solution: **

Sum of digits = (4 + 8 + 1 + *x* + 6 + 7 + 3) = (29 + x), which must be divisible by 9.

*x* = 7.

Workspace

Report

The difference between the local value and the face value of 7 in the numeral 32675149 is

**A. ** 75142

**B. ** 64851

**C. ** 5149

**D. ** 69993

**E. ** None of these

**Answer : ****Option D**

**Explaination / Solution: **

(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993

(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993

Workspace

Report